Mode-synthesizing atomic force microscopy and mode-synthesizing sensing

ABSTRACT

A method of analyzing a sample that includes applying a first set of energies at a first set of frequencies to a sample and applying, simultaneously with the applying the first set of energies, a second set of energies at a second set of frequencies, wherein the first set of energies and the second set of energies form a multi-mode coupling. The method further includes detecting an effect of the multi-mode coupling.

This application is a divisional application of U.S. patent applicationSer. No. 12/726,083, filed Mar. 17, 2010, titled Mode-SynthesizingAtomic Force Microscopy and Mode-Synthesizing Sensing (currentlypending), the entire disclosure of which is incorporated herein byreference.

This invention was made with government support under Contract No.DE-AC05-000R22725 awarded by the U.S. Department of Energy. Thegovernment has certain rights in the invention.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates generally to an analysis system and moreparticularly to a mode-synthesizing atomic force microscopy system.

2. Discussion of Related Art

Atomic Force Microscopy

Non-destructive, nanoscale characterization techniques are needed tounderstand both synthetic and biological materials. Atomic forcemicroscopy (AFM) is a well established technique for imaging surfacefeatures with nanometer or even sub-nanometer resolution. In atomicforce microscopy, a cantilever with a small spring constant is draggedon the surface of a sample. The cantilever has a probe tip capable ofcontacting the sample with a nanometer contact area. The contact forcebetween the tip and the sample includes short range forces, such as thevan der Walls force. Therefore, any small variation in distance betweenthe probe tip and the surface of the sample can result in a large changein the force due to the short range nature of the forces.

When the cantilever is rastered on the top of the surface of the sample,the tip experiences attractive and repulsive forces that depend on thechemical and mechanical properties of the sample. For example,deflection of the cantilever generates a response that creates a spatialforce image of the surface with nanometer spatial resolution. However,conventional atomic force microscopy is limited only to surfacetopography.

Ultrasonic Force Microscopy

In the so-called ultrasonic force microscopy, a microcantilever or asample is coupled to a mechanical oscillator that drives themicrocantilever (or a sample) at a frequency f. The microcantilever hasa probe tip that interacts with a surface of a sample. An image may thenbe acquired from the amplitude and phase of a signal that results fromlocking onto the cantilever motion with reference to the acoustic wavefrequency. Ultrasonic microscopy has been used to study the elasticproperties of various materials.

Scanning Near Field Ultrasound Holography (SNFUH)

While atomic force microscopy provides no information concerning thesubsurface features of a sample, this limitation can be overcome by therecent development of Scanning Near Field Ultrasound Holography (SNFUH)by Shekawat and Dravid, which can also differentiate materials ofdifferent mechanical properties. This technique has recently been shownproficient for localization of embedded nanoparticles in cells, whereagglomerated carbon nanohorns and synthesized silica nanoparticlesburied in a mouse macrophage were visualized. The sample holder of anatomic force microscope is modified to accommodate a piezoelectriccrystal that is vibrated at MHz frequencies. The ultrasonic wavestraveling through the sample influence the motion of the atomic forcemicroscope's cantilever that is in contact with the surface of thesample. Since the atomic force microscope's cantilever is independentlyvibrated by a second piezoelectric crystal at a different frequency thanthe ultrasonic waves generated by the first piezoelectric crystal, thesystem creates a new mode at the difference frequency that can bemonitored using a position sensitive detector (PSD) of the atomic forcemicroscope. When the phase of the signal with respect to the differencein the exciting frequencies of the two piezoelectric crystals isdisplayed as a function of spatial location of the scanning cantilevertip, the phase image map shows contrast due to acoustic impedancevariation and material inhomogeneity of the subsurface or surfacefeatures.

OBJECTS AND SUMMARY OF THE INVENTION

A first aspect of the present invention regards an analysis system thatincludes a first excitation source that applies to a sample a first setof energies at a first set of frequencies. The analysis system furtherincludes a second excitation source, independent of the first excitationsource, that applies a second set of energies at a second set offrequencies to a probe, wherein the first set of energies and the secondset of energies are simultaneously applied to the sample and the probe,respectively, and form a multi-mode coupling. The analysis systemincludes a detector that detects dynamics of the probe from which aneffect of the multi-mode coupling can be obtained.

A second aspect of the present invention regards a method of analyzing asample that includes applying a first set of energies at a first set offrequencies to a sample and applying, simultaneously with the applyingthe first set of energies, a second set of energies at a second set offrequencies to a probe, wherein the first set of energies and the secondset of energies form a multi-mode coupling. The method further includesdetecting an effect of the multi-mode coupling.

A third aspect of the present invention regards a sensor system thatincludes a first cantilever having a first end and a first excitationsource that applies to the first cantilever a first set of energies at afirst set of frequencies. The system further includes a secondcantilever having a second end, wherein the second end is adjacent tothe first end and a second excitation source, independent of the firstexcitation source that applies a second set of energies at a second setof frequencies. The first set of energies and the second set of energiesare simultaneously applied to the first cantilever and the secondcantilever, respectively, and form a multi-mode coupling. The systemfurther includes a detector that detects an effect of the multi-modecoupling.

A fourth aspect of the present invention regards a method of analyzing asample that includes applying a first set of energies at a first set offrequencies to a sample via a first cantilever and applying a second setof energies at a second set of frequencies to the sample via a secondcantilever, wherein the first and second cantilevers are adjacent to oneanother. The first set of energies and the second set of energies aresimultaneously applied to the first cantilever and the secondcantilever, respectively, and form a multi-mode coupling. The methodfurther includes detecting an effect of the multi-mode coupling.

A fifth aspect of the present invention regards an analysis system thatincludes a first excitation source that applies to a sample a first setof energies at a first set of frequencies and a second excitationsource, independent of the first excitation source, that applies asecond set of energies at a second set of frequencies to the sample. Thefirst set of energies and the second set of energies are simultaneouslyapplied to the sample, and form a multi-mode coupling. The analysissystem further including a probe that contacts the sample and a detectorthat detects dynamics of the probe from which an effect of themulti-mode coupling can be obtained.

A sixth aspect of the present invention regards a method of analyzing asample that includes applying a first set of energies at a first set offrequencies to a sample and applying simultaneously with the applyingthe first set of energies a second set of energies at a second set offrequencies to the sample. The first set of energies and the second setof energies form a multi-mode coupling. The method further includesdetecting an effect of the multi-mode coupling via a probe that contactsthe sample.

One or more advantages that are present in one or more aspects of thepresent invention are:

access to new mechanical information on the sample;

gentleness to soft samples;

takes advantage of the nonlinear nature of the probe-sample interaction;

simultaneous image acquisition; and

surface and subsurface information.

Further characteristics and advantages of the present invention willbecome apparent in the course of the following description of anexemplary embodiment by the drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically shows a first embodiment of an analysis system inaccordance with the present invention;

FIG. 2 shows a 3-stimuli (two for the probe and one for the sample)diagram representing all dynamic states created by a representativecoupling C generated by the analysis system of FIG. 1;

FIG. 3 schematically shows a second embodiment of an analysis system inaccordance with the present invention;

FIG. 4 shows a plot of eigenfrequency vs. eigenmode number for differenttypes of probes that can be used with the systems of FIGS. 1-3 and 6-12

FIGS. 5 a-d show spectral and amplitude dependencies for variousselected C-modes using the analysis system of FIG. 3;

FIGS. 6 a-j show simultaneous C-mode imaging of a sample using theanalysis system of FIG. 3 and corresponding modes excited in the systemand used for imaging (FIGS. 6 e(1)-(4), f(1)-(4));

FIG. 7 schematically shows an embodiment of a sensor system inaccordance with the present invention;

FIG. 8 schematically shows a third embodiment of an analysis system inaccordance with the present invention;

FIG. 9 schematically shows a fourth embodiment of an analysis system inaccordance with the present invention;

FIG. 10 schematically shows a fifth embodiment of an analysis system inaccordance with the present invention;

FIG. 11 schematically shows a sixth embodiment of an analysis system inaccordance with the present invention;

FIG. 12 schematically shows a seventh embodiment of an analysis systemin accordance with the present invention;

FIG. 13 schematically shows an eighth embodiment of an analysis systemin accordance with the present invention;

FIG. 14 A shows a plot of surface traction of a sample with nanoparticleinhomogenities;

FIG. 14 B shows a plot of surface velocity of a sample with nanoparticleinhomogenities;

FIG. 14C shows the sample from which the plots of FIGS. 14A-B arederived;

FIGS. 15 a-j show MSAFM images of a sample with nanostructures formedthereon using the system of FIG. 3;

FIGS. 16 a-d show topography images of a cross-section of the sampleused in FIGS. 6 a-j using standard AFM imaging;

FIG. 17 shows an MSAFM image of a sample using the system of FIG. 3;

FIG. 18 a shows a topography image of a sample using standard AFMimaging; and

FIG. 18 b shows an MSAFM image of the sample of FIG. 18 a using thesystem of FIG. 3.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In the embodiments of the invention described hereinafter, like numeralswill be used to identify like elements. Before going into the details asto the various embodiments of the present inventions, the generalprinciples of the inventions, as presently understood, are discussedbelow. In particular, the present invention regards variations on atomicforce microscope systems and techniques of their use that can obtain arange of surface and subsurface information by exploiting the nonlinearnanomechanical coupling between the cantilever probe and the sample.These systems and techniques come under the guise of so-calledmode-synthesizing atomic force microscopy (MSAFM), which relies onmulti-harmonic forcing of the sample and the probe. A rich spectrum offirst- and higher-order couplings is accessible, providing a multitudeof new operational modes for atomic force microscopy. The capabilitiesof the systems and techniques can be demonstrated by examiningnanofabricated samples and plant cells.

In MSAFM, a silicon microcantilever 114 interacts with a surface ofinterest of a sample 102 via a van der Waals potential (and often withcontributions from other interactions such as thermomolecular,electrostatic, Casimir, etc.) prevailing in the nanometer interfacialregion between the surface r_(s) and the cantilever probe tip 112located at r_(L) relative to origin O, as partially shown in FIG. 1. Theleft boundary of the microcantilever 114 (length L) is fixed withrespect to the origin r_(o) of the accelerated reference frame 0′ x′ y′,but oscillates with respect to the inertial reference frame Oxy. Themicrocantilever 114 is driven by mechanical oscillator, such as PZT film116, at a frequency f_(p) so as to exert a force F_(p) on themicrocantilever 114. Similarly, the sample 102 is driven by PZT filmoscillator 108 at a frequency f_(s) so as to generate a force F_(s) onthe sample 102. The forces F_(p) and F_(s) result in the excitation ofan elastic mode of the sample 102 and the microcantilever 114.

The motion of the sample 102 that is subjected to frequency f_(s) ismeasured with respect to reference frame Oxy shown in FIG. 1. Suchmeasurement is accomplished by use of a light source, such as a laserdiode 118, that generates a beam 120 of light directed toward themicrocantilever 114 and is reflected toward a detector, such as afour-quadrant position sensitive photodetector 122. The laser 118 andthe position sensitive photodetector 122 are used to measure thedynamics of the system in time domain by generating a signal S(t). Anembedded inhomogeneity at r_(si) modifies the dynamics of r_(s)affecting the signal S(t) through a multiple-order coupling C that issolely induced by a nonlinear interaction between the microcantileverprobe 114 and the sample 102. The wavelength of the high frequency ω_(p)oscillations of the microcantilever 114 is denoted by λ_(p).

The multiple-order coupling C is provided by the much faster (than theexcitation time scales) interfacial electronic interactions. Thecoupling C allows synthesis of a multitude of new operational modes, orC-modes, limited only by the system and measurement bandwidth. The vastdynamic landscape of the multiple-order coupling C renders MSAFM to bedrastically different than existing modalities. To better describe thesynthesized modes, a Dirac-like notation is introduced for the states ofthe system (C-modes) and arrange in a Groterian-like diagram as shown inFIG. 2.

MSAFM is founded upon exerting a multi-harmonic force F_(s) on thesample 102. Similarly, a multi-harmonic force F_(p) is applied to themicrocantilever 114. The two forces are given below:

F _(s) =F _(s)=Σ_(j) a _(s,j) sin(2πf _(s,j) t+φ _(s,j))  1)

F _(p) =F _(p)=Σ_(i) a _(p,i) sin(2πf _(p,i) t+φ _(p,i)),  2)

wherein when the microcantilever 114-sample 102 separationd(=|r_(L)−r_(s)|) is reduced beyond a threshold, the nonlinear andnonzero interaction C creates a time domain signal S(t) that representsthe dynamic state of the microcantilever 114, as shown in FIG. 1.

In general, the system shown in FIG. 1 is a two oscillator system. Thereis an example in atomic physics of a system that involves twooscillators that is helpful in explaining the coupling process of thesystem shown in FIG. 1. In particular, in the case of a hydrogen atom,the electron and the nucleus constitute two oscillators that interactwith one another via a Coulomb potential to generate the discretequantum states lnlm>. In an analogous manner, MSAFM has two oscillators,the microcantilever probe 114 and the sample 102, that interact via avan der Waals potential so as to generate the well-defined statesln_(v)m_(v)l_(v) . . . >. The number of excitation states determine thenumber of integers (n_(v), m_(v), l_(v), . . . ), which will populate agiven state l•>. Then assigning n, m, l, . . . =0, ±1, ±2, . . . , andan index v=s, p, where s and p refer to the sample 102 and themicrocantilever probe 114, respectively, the term ln_(v)m_(v)l_(v) . .. > denotes a state with a frequency ω_(|nvmvlv) . . .>=n_(v)ω_(v,1)+n_(v)ω_(v,2)+l_(v)ω_(v,3)+ . . . and an amplitudea_(|nvmvlv) . . . >, where ω_(v,i)=2πf_(v,i). Now, representing eachFourier component of the signal S, symbolically as ln_(v)m_(v)l_(v) . .. >, MSAFM utilizes the amplitude and phase of S(t), by simultaneouslylocking onto the frequency of any given number of C-modes, that is,ω_(|nvmvlv . . . >.)

As an application of the above theory, suppose i=1, 2 and j=1 in F_(p)and F_(s), a striking 62 C-modes are predicted as mapped in FIG. 2.Here, a selected 34 experimentally measured C-modes are also shown, forwhich the contour plots in the fifth column collectively represent themeasured amplitudes amplitude a_(|nvmvlv) . . . > as a function of theamplitude of the excitations. The first order coupling C⁰, mixes thethree excitation modes l0_(p)0_(p)1_(s), >, l0_(p)1_(p)0_(s),> and modesl1_(p)0_(p)0_(s),> to give rise to 6 modes via sum and differencegeneration, whereas the second order coupling C¹ mixes the previousmodes to create the 62 modes by further sum and difference generation.Consequently, the coupling C may be envisioned as being analogous to thesusceptibility χ in nonlinear optics, albeit the role of a materialnonlinear polarizability is played by the nonlinear interfacial forcesin MSAFM. Juxtaposition of the modes in the proposedGroterian-resembling diagram, in fact surpasses a simple storingutility. The diagram clearly keeps track of whether a given mode is aresult of a summation or subtraction, and whether the mode is a resultof a first coupling or a higher order coupling. In addition, the diagramalso includes the information about the origin of the excitation (p forprobe, s for sample). Furthermore, the modes are vertically dispersedaccording to their frequency.

It should be noted that while FIG. 1 shows one set of vibrationalenergies/frequencies applied to the microcantilever 114 and another setto the sample 102, an advantage of the present invention is the creationof the multi-mode coupling effect mentioned previously. Accordingly, thepresent invention encompasses systems that generate excitationenergies/frequencies via other means, such as electromagneticoscillations, and applying multiple excitation energies/frequencies tothe sample 102.

In summary, the analysis system described above with respect to FIGS.1-2 presents a new modality of force microscopy that can be ofsignificant importance for nanoscale characterization of material.Exploiting the nonlinear interactions, in a single run, MSAFM is capableof delivering a myriad (FIG. 2) of nanoscale features not previouslyattainable. Controlled use of the synthesized modes for surface andsubsurface characterization of poplar cells, per the discussion tofollow regarding FIGS. 5 a-h, demonstrate the versatility of themethodology presented herein and suggest potential application instudying complex samples, such as an organic system that exhibits avariety of interrelated chemical, morphological, and mechanicalproperties, as opposed to simple samples characterized rather withhomogeneity, uniformity, and isotropicity. It is believed that bothattractive and repulsive forces are at play under MSAFM. In addition,within the measurement bandwidth, the C^(β) modes are all fullyoperational. MSAFM capitalizes on the full range of coupling C, andutilizes both amplitude and phase towards image formation, and thereforemany opportunities remain to be explored.

With the above discussion of the theory behind the present invention inmind, there are several embodiments possible to exploit the presentinvention. For example, an analysis system 100 is shown in FIG. 3. Inthis embodiment, the sample 102 is attached to a piezoelectric sampleholder 104 capable of applying a first set of vibrational energies byvibrating the sample 102 at a few kHz to several tens of MHzfrequencies. The sample holder 104 includes a base 106 and a firstexcitation source, such as a bimorph/piezoelectric crystal (PZT)oscillator 108. The PZT oscillator 108 is glued to the base 106 at alocation that enables excitation of the sample 102 from the bottom ofthe sample 102, in order to access subsurface information. Thefrequencies generated by the PZT oscillator 108 can be in the range of afew kHz to tens of MHz, wherein the limit on its frequency is imposed bythe bandwidth of the other pieces of equipment of the system 100.

The sample can be either organic or inorganic in nature. In the case ofan organic sample, examples of the sample can be materials important forbioenergy production, such as Populus. The thickness of the samples canbe varied from a fraction of a μm (micrometer) to several tens of μm.The sample and the glass slides are immobilized on the base 106 usingglue or an adhesive film typically used in Scanning Electron Microscopy.

As shown in FIG. 3, the sample 102 is in contact with a tip 112 of amicrocantilever 114 that collectively define a probe of an atomic forcemicroscope (AFM). The position of the probe with respect to the samplebase 106 can be changed in the x-y direction (depending on the AFMsystem used, either the cantilever 114 or the sample 102 can be moved inx-y direction). The AFM can be a commercial product such as theMultimode system made by Veeco with a Nanoscope III controller. As shownin FIG. 3, a second excitation source, such as a PZT oscillator 116, iscoupled to the microcantilever 114. A light source, such as laser diode118, generates a beam 120 of light that is directed toward themicrocantilever 114 and is reflected toward a detector, such as afour-quadrant photodetector 122. The reflected beam contains informationregarding the deflection undergone by the microcantilever 114. A mirroror other optical elements may direct the reflected light toward thephotodetector 122. Besides the above described optical deflectionsystem, it would be possible to use a piezoresistive or piezoelectricmethod, in which case the microcantilever 114 would be of differentcomposition.

In operation, the PZT oscillator 108 is controlled by n functiongenerators FG_(is) (i=1, 2, 3, . . . n) represented collectively by box126 so that the PZT oscillator 108 generates multiple vibrationalenergies in the form of waves at multiple frequencies f_(is) andamplitude a_(s). The waves have frequencies f_(is) that range from a fewkHz to several tens of MHz. The waves travel through the sample 102 andare sensed up by the microcantilever 114. The amplitude and phase of awave at a given frequency are detected via the motion of the tip 112.Note that function generators FG_(is) 126 can be replaced by a singleprogrammable function generator that can handle multifrequencywaveforms.

As shown in FIG. 3, a second PZT oscillator 116 is glued to themicrocantilever 114. The PZT oscillator 116 is connected to n functiongenerators FG_(ip) (i=1, 2, 3, . . . n) represented collectively by box136 so that the PZT oscillator 116 generates multiple vibrationalenergies in the form of waves at multiple frequencies f_(ip) andamplitude a_(p). The frequencies f_(ip) are generated independently ofthe frequencies f_(is). The frequencies f_(ip) range from a few kHz toseveral tens of MHz. In order to read out the deflection of themicrocantilever 114, the optical detection system is generally used asdescribed previously. Motion of the tip 112 can also be detected by thepiezoresistive method or the piezoelectric method described previously.Note that function generators FG_(ip) 136 can be replaced by a singleprogrammable function generator that can handle multifrequencywaveforms.

Note that the oscillators 108 and 116 may be PZT films available fromPhysik Instrumente (model PIC255). Both films can be wirebonded toaccept multiple driving waves from the function generators 126, 136.Using a network analyzer, impedance measurements can be carried out toobtain the frequency response of the PZT oscillators 108 and 116 anddetermine their resonances. Such information is needed for thedetermination of the total experimental and measurement bandwidth andalso for quantitative measurements.

In addition, the microcantilever 114 may be selected to have differentstiffnesses and geometries. In the case of a soft microcantilever, itcan, for example, have a stiffness of 0.06 N/m that has a triangulargeometry. An example of such a microcantilever is model DNP-S availablefrom Veeco Probes. The soft microcantilever can be made of siliconnitrite with a gold coating. In the case of a stiff microcantilever,such a microcantilever can have a rectangular geometry and be made ofsilicon. An example of a stiff microcantilever is made by Olympus (modelOMCL-AC160 TS-W2).

The resonances in the oscillatory motion of the microcantilevers 114 canbe obtained analytically for simpler geometries, and computationallyotherwise. For example, the eigenfrequencies and eigenmodes of bothrectangular (stiff) and triangular (soft) silicon cantilevers 114 can becalculated as shown in FIG. 4. Note that the microcantilever 114possesses an infinite number κ=1, 2, . . . of eigenmodes, some of whichcan resonantly be excited. Thus, by the resonance frequency, itcorresponds to an actual excited eigenmode of the probe, whereas theoff-resonance response of the cantilever 114 is only a result of thepropagation of the forced oscillations of the piezoelectric bimorph. InMSAFM, the motion of the left boundary of the cantilever 114, as shownin FIG. 1, appears as a time dependent function representing a drivingterm in the partial differential equation that describes the dynamics ofthe probe in the stationary system Oxyz in FIG. 1.

The free spectra of the used cantilevers, that is, for a largeprobe-sample separation (d=|r_(L)−r_(s)| large in FIG. 1) and (a_(s),a_(p))=(0, 0) (both piezoelectric crystals turned off), are measured tobe f_(p) ^(k)=(23, 144, 403, 790, 1307, . . . ) kHz for a soft probewith a spring constant k=0.06 N/m, and f_(p) ^(k)=(380, 1800, . . . )kHz for a stiff probe with spring constant k=42 N/m, which is inagreement with the computational results of FIG. 4. The computedeigenfrequencies and eigenmodes of FIG. 4 regard the situations thatinvolve a stiff rectangular probe that is 160 μm long, 50 μm wide, and4.6 μm thick, and a soft triangular cantilever that is 180 μm long, 18μm wide, and 0.6 μm thick. As expected, for the same eigenmode number,the stiff probe exhibits much faster dynamics. The insets show thecomputationally determined transversal mode-shapes at selectedeigenfrequencies. The shaded scale restates the deformation of theprobes.

A coupling C, such as that described previously, is achieved by theanalysis system 100. The coupling C is determined from the signal S(t)generated by detector 122. The controller 138 monitors the feedback loopthat controls the Z-position of the microcantilever 114 and converts thesignal S(t) into display of a 2D image. The signal is sent to a spectrumanalyzer 145 to identify the spectrum of frequencies representative ofthe multi-order coupling in the Fourier space. The signal is sent to alock-in amplifier 140 as well to monitor the amplitude and phase a givencomponent of the S(ω) (i.e. one of the peaks observed on the spectrumanalyzer), relative to the nonlinear multi-order coupling resulting fromthe excitation of the microcantilever 114 and the sample 102 brought incontact with one another. The lock-in amplifier 140 sends amplitude andphase information/signals to a processor 141 (the processor 141 may beincluded in the controller 138) that determines an image of the sample102 corresponding to the response of the system at the given frequencyused as reference in the lock-in amplifier 140. The spectrum determinedby spectrum analyzer 145 and the image of the sample 102 determined byprocessor 141 can be displayed on display 143.

Other analyses performed by the analysis system 100 are possible. Forexample, the system 100 can be operated using the AFM and dataacquisition software such as Labview, and a Signal Access Module (SAMfrom Veeco), which allow external signals to be sent back to thecontroller 138 to be displayed at display 143. The information providedthrough the AFM software is: 1) the topography of the sample, 2) theresponse of the sample to the mechanical oscillations for each component(frequency) generated by the nonlinear coupling. The informationprovided through the data acquisition system software will include mapsof the contribution of a given frequency to the complex coupling betweenthe tip 112 of the microcantilever 114 and the sample 102. This willinclude amplitude and phase measurements with respect to the C-modesover the (driving) frequency ranges and (driving) amplitudes ranges. Itcan also include monitoring of the evolution of the amplitude and phaseof the signal at a given frequency as a function of the position of themicrocantilever 114 with respect to position (X, Y, Z) of the sample 102or with respect to time. The study of the deflection of themicrocantilever 114 as a function of Z is commonly called a “force curvemeasurement” and is used to study the mechanical properties of thesample 102.

Using the analysis system 100, the parameter dependence of selectedC-modes can be demonstrated. For example, FIG. 5 a shows for fixed andequal driving amplitudes a_(p,1)=a_(s,1), the variation of the amplitudeof the C⁰-mode l-1_(s)1_(p)> for f_(l-1s1p>) varying from 25 kHz to 1MHz. FIG. 5 b shows amplitude dependence of the C⁰-mode l1_(s) 1 _(p)>for f_(l1s1p>) varying from 100 kHz to 1.5 MHz at higher excitationamplitudes. FIGS. 5 c-d show the dependence of selected C¹-modes(|2_(s)-1_(p)> (c), and |−1_(s)2_(p)> (d)) upon the excitation frequencyfor f_(l2s-1p>) and f_(l-1s2p> varying from) 50 kHz to 1.5 MHz. Theexcitation amplitudes are annotated on the top portion and a scale baris provided to categorize the contour levels. The exhibited bands can beidentified to correspond to (in-contact) ω^(κ), κ=1, 2, . . . . Thevertical lines formed in FIGS. 5 a-d are indicative of a maximum in thedisplacement of the microcantilever 114 at any of the ω_(|nm)> when thedriving frequency applied to the probe corresponds to one of the ω^(κ).For example, the vertical lines V_(b), V_(c) and V_(d) of FIGS. 5 b-d,respectively, denote cases wherein the frequency f_(|0s1p>) matches aresonance frequency of the microcantilever. The diagonal lines D_(a-d)denote the states |f_(1s)−f_(1p)>, |f_(1s)+f_(1p>), |2f_(1s)−f_(1p>),and |2f_(1p)−f_(1s>), respectively, matching with a resonance frequencyof the microcantilever. The horizontal line H_(d) of FIG. 5 d denote acase wherein the frequency f_(|1s 0p>) matches a resonance frequency ofthe microcantilever.

To demonstrate how MSAFM analysis system 100 can successfully access newdimensions of sample information, suppose two sets of C-modes are usedto image various layers of the cell walls of a sample made of poplarwood. FIGS. 6 a-h show contour plots of partial spectral windowscontaining the invoked C-modes. In the first set, shown in FIGS. 6(a-d), the participant modes include lnm>=|−1_(s)1_(p)> [FIGS. 6(a,e(1))], |−1_(s)2_(p)> [FIGS. 6( b,e(2))], |1_(s)1_(p)> [FIGS. 6(c,e(3))], and |0_(s)2_(p)> [FIG. 6( d,e(4))] originating from i=j=1,while FIGS. 6( g-j) display images acquired by |nm)=|−1_(p) 1_(p)>[FIGS. 6( g,f(1))], |2_(p)−1_(p)> [FIGS. 6( h,f(2))], |−1_(p)2_(p)>[FIGS. 6( i,f(3))], and |0_(p)2_(p)> [FIGS. 6( j,f(4))] originating fromi=1, 2, and j=0 (i.e., no subsurface contribution). As shown in FIG. 6b, the secondary cell wall (SCW), the cell corner (CC), and the middlelamella (L), reveal distinct features of the complex organic matrix. Thecenter frequency for each window in FIGS. 6( e(1)-(4),f(1)-(4)) appearsbelow the frequency axis. In FIGS. 6( f-j), the C-modes from theexcitation of the probe with two independent waves but maintaining astationary sample. The cell wall regions and the lamella can beidentified from the complementary information contained by each image.

Another analysis system is shown in FIG. 7. As shown in FIG. 7, sensorsystem 200 is a variation of analysis system 100, wherein sample 102 hasbeen replaced by a second microcantilever 214 that may or may notinclude a tip 212. Accordingly, the molecules in the environment will be“the sample.” The spacing between the microcantilevers 114 and 214 isnot more than a few tens of nanometers.

As mentioned previously, the sensor system 200 includes a secondmicrocantilever 214. An excitation source, such as PZT oscillator 108,is glued to an end of the second microcantilever 214 opposite to the endat which the tip 212 is attached. The PZT oscillator 108 can generatevibrational energies having frequencies in the range of a few kHz totens of MHz, wherein the limit on its frequency is imposed by thebandwidth of the other pieces of equipment of the system 200.

A light source, such as laser diode 218, generates a beam 220 of lightthat is directed toward the microcantilever 214 and is reflected towarda detector, such as a four-quadrant photodetector 222. The reflectedbeam contains information regarding the deflection undergone by themicrocantilever 214. A mirror or other optical elements may direct thereflected light toward the photodetector 222. Besides the abovedescribed optical deflection system, it would be possible to use apiezoresistive or piezoelectric method, in which case themicrocantilever 214 would be of different composition.

As shown in FIG. 7, the microcantilever 214 is in contact with a tip 112of a microcantilever 114 of an atomic force microscope (AFM). The AFMcan be a commercial product such as the Multimode system made by Veecowith a Nanoscope III controller (but it is not restricted to thismodel).

As shown in FIG. 7, another excitation source, such as a PZT oscillator116, is coupled to the microcantilever 114. A light source, such aslaser diode 118, generates a beam 120 of light that is directed towardthe microcantilever 114 and is reflected toward a detector, such as afour-quadrant photodetector 122. The reflected beam contains informationregarding the deflection undergone by the microcantilever 114. A mirroror other optical elements may direct the reflected light toward thephotodetector 122. Besides the above described optical deflectionsystem, it would be possible to use a piezoresistive or piezoelectricmethod, in which case the microcantilever 114 would be of differentcomposition.

In operation, the PZT oscillator 108 is controlled by n functiongenerators FG_(is) (i=1, 2, 3, . . . n) represented collectively by box126 so that the PZT oscillator 108 vibrates the microcantilever atmultiple vibrational energies having frequencies f_(is) and amplitudea_(s). The frequencies f_(is) range from a few kHz to several tens ofMHz. In order to read out the deflection of the microcantilever 214, theoptical detection system is generally used as described previously.Motion of the tip 212 can also be detected by the piezoresistive methodor the piezoelectric method described previously. Note that functiongenerators FG_(is) can be replaced by a single programmable functiongenerator that can handle multifrequency waveforms.

As shown in FIG. 7, the PZT oscillator 116 is glued to themicrocantilever 114. The PZT oscillator 116 is connected to n functiongenerators FG_(ip) (i=1, 2, 3, . . . n) represented collectively by box136 so that the PZT oscillator 116 generates multiple vibrationalenergies in the form of waves at multiple frequencies f_(ip) andamplitude a_(p). The frequencies f_(ip) are generated independently ofthe frequencies f_(i). The frequencies f_(ip) range from a few kHz toseveral tens of MHz. In order to read out the deflection of themicrocantilever 114, the optical detection system is generally used asdescribed previously. Motion of the tip 112 can also be detected by thepiezoresistive method or the piezoelectric method described previously.Note that function generators FG_(ip) can be replaced by a singleprogrammable function generator that can handle multifrequencywaveforms.

Couplings C, such as that described previously, are achieved by thesensor system 200. The couplings C are determined from the signals S(t),T(t) generated by detectors 122 and 222, respectively. The signals aresent to the controllers 138 and 238 to control the Z-position of theprobes as part of a feedback loop. The signals are also sent to lock-inamplifiers 140 and 240 to monitor the contribution of nonlinearmulti-order coupling resulting from the excitation of themicrocantilever 114 and the microcantilever 214 brought in contact withone another. The signals are also sent to spectrum analyzer 145 andspectrum analyzer 245 to measure a spectrum of multi-order couplingassociated with each cantilever. The lock-in amplifiers 140 and 240monitor the contribution of a given component of the coupling (a C-mode)in the form of its amplitude and phase, and the information/signals canbe sent to respective processors 141 and 241 for further analysis. Thespectra determined by the spectrum analyzers 145 and 245 and the imagesdetermined by processors 141 and 241 can be displayed on displays 143and 243.

Other analyses performed by the sensor system 200 are possible. Forexample, the system 200 can be operated using the AFM and dataacquisition software such as Labview and a Signal Access Module (SAMfrom Veeco), which allow external signals to be sent back to thecontrollers 138, 238 to be displayed at displays 143, 243. Theinformation provided through the AFM software includes maps of thecontribution of a given frequency to the complex coupling between themicrocantilever 114 and the microcantilever 214. This will includeamplitude and phase measurements with respect to a given frequency tothe complex coupling between the microcantilever 114 and themicrocantilever 214. It can also include monitoring of the evolution ofthe amplitude and phase of the signal at a given frequency as a functionof the position of the microcantilever 114 with respect to the position(X, Y, Z) of the microcantilever 214. The study of the deflection of themicrocantilever 114 as a function of Z is used to study the mechanicalproperties of the molecules present between the tip 112 and 212. Thegeneral use of the sensor system 200 is as a sensitive multi frequencyoscillator. Adsorption of small number of molecules will result in aseries of shifts in the frequencies that can be monitored.

Another analysis system is shown in FIG. 8. As shown in FIG. 8, analysissystem 300 is a variation of analysis system 100, wherein PZToscillators 108 and 116 have been removed and replaced with conductivematerials, as explained below, in order to exploit the electrostaticforces of the system (instead of Van der Walls in 100 and 200 systems).In this embodiment, an organic or inorganic sample 102 is attached to asample holder 304 capable of generating excitation electromagneticenergies applied to the sample 102 at a few kHz to several tens of MHzfrequencies. The vibrations are generated by driving the electricallyconductive layers 308 and 316 with varying the electric fields. Thesample holder 304 includes a base 106 and an electrically conductivelayer 308 that acts as a first excitation source. The position of theprobe 112-114 with respect to the sample base 106 can be changed in thex-y direction (depending on the AFM system used, either the cantileveror the sample can be moved in x-y direction). The layer 308 is glued tothe base 106 at a location that enables excitation of the sample 102from the bottom of the sample 102, in order to access subsurfaceinformation. The layer 308 generates electric fields that oscillate inthe range of a few kHz to tens of MHz, wherein the limit on itsfrequency is imposed by the bandwidth of the other pieces of equipmentof the system 300.

As shown in FIG. 8, the sample 102 is in contact with a tip 112 of amicrocantilever 114 of an atomic force microscope (AFM). The AFM can bea commercial product such as the Multimode system made by Veeco with aNanoscope III controller (but it is not restricted to this model). Asshown in FIG. 8, at least an end portion of the microcantilever 114includes a second excitation source, such as an electrically conductivematerial 316, which can cause the microcantilever 114 to vibrate. Theentire cantilever 114 is electrically conductive so that electricalforce component is generated at the tip 112. A light source, such aslaser diode 118, generates a beam 120 of light that is directed towardthe microcantilever 114 and is reflected toward a detector, such as afour-quadrant photodetector 122. The reflected beam contains informationregarding the deflection undergone by the microcantilever 114. Suchdeflection reflects the interaction between the sample 102 and the tip112 and can include van der Waals-type and Coulomb-type contribution,wherein the Coulomb-type contribution may be dominant depending on thestrength of the electric fields. A mirror or other optical elements maydirect the reflected light toward the photodetector 122. Besides theabove described optical deflection system, it would be possible to use apiezoresistive or piezoelectric method, in which case themicrocantilever 114 would be of different composition.

In operation, the electric fields caused by layer 308 are controlled byn function generators FG_(is) (i=1, 2, 3, . . . n) representedcollectively by box 126 so that the conductive sample holder 308generates multiple electric fields at multiple frequencies f_(is) andamplitude a_(s). The electric fields have frequencies f_(is) that rangefrom a few kHz to several tens of MHz. The multi-mode interactionbetween the electric fields generated by the layer 308 and material 316are sensed up by the microcantilever 114. Note that function generatorsFG_(is) can be replaced by a single programmable function generator thatcan handle multifrequency waveforms.

As shown in FIG. 8, the electric fields generated by electricallyconductive material 316 are controlled by n function generators FG_(ip)(i=1, 2, 3, . . . n) represented collectively by box 136 so that thematerial 316 generates multiple electric field energies having electricfields with multiple frequencies f_(ip) and amplitude a_(p). Thefrequencies f_(ip) are generated independently of the frequenciesf_(is). The frequencies f_(ip) range from a few kHz to several tens ofMHz. In order to read out the deflection of the microcantilever 114, theoptical detection system is generally used as described previously.Motion of the tip 112 can also be detected by the piezoresistive methodor the piezoelectric method described previously. Note that functiongenerators FG_(ip) can be replaced by a single programmable functiongenerator that can handle multifrequency waveforms.

A coupling C, such as that described previously, is achieved by theanalysis system 300. The coupling C is determined from the signal S(t)generated by detector 122. The signal is sent to the controller 138 tocontrol the Z-position of the probes as part of a feedback loop. Thesignal is also sent to a lock-in amplifier 140 to monitor the nonlinearmulti-order coupling resulting from the excitation of themicrocantilever 114 and the sample 102 brought in contact with oneanother. The signal is sent to a spectrum analyzer 145 as well tomeasure a spectrum of multi-order coupling in a manner similar to thatdone with analysis system 100. The lock-in amplifier 140 sends amplitudeand phase information/signals to a processor 141 that determines animage of the sample 102 based on the signals in a manner similar as donein analysis system 100. The spectrum determined by spectrum analyzer 145and the image of the sample 102 can be displayed on display 143.

Other analyses performed by the analysis system 300 are possible. Forexample, the system 300 can be operated using the AFM and dataacquisition software such as Labview and a Signal Access Module (SAMfrom Veeco), which allow external signals to be sent back to thecontroller 138 to be displayed at display 143. The information providedthrough the AFM software are: 1) the topography of the sample and 2) theresponse of the sample to the electric field oscillations for eachcomponent (frequency) generated by the nonlinear coupling. Theinformation provided through the data acquisition system software willinclude maps of the contribution of a given frequency to the complexcoupling between the tip 112 of the microcantilever 114 and the sample102. This will include amplitude and phase measurements with respect toa given frequency to the complex coupling between the tip 112 of themicrocantilever 114 and the sample 102. It can also include monitoringof the evolution of the amplitude and phase of the signal at a givenfrequency as a function of the position of the microcantilever 114 withrespect to position (X, Y, Z) of the sample 102 or as a function oftime. The study of the deflection of the microcantilever 114 as afunction of Z can also be used to study the mechanical properties of thesample 102.

Another analysis system is shown in FIG. 9. As shown in FIG. 9, analysissystem 400 is a variation of analysis system 100, wherein a metal layer402 is introduced between the organic or inorganic sample 102 and thePZT oscillator 108. In this embodiment, the sample 102 is attached to apiezoelectric sample holder 404 capable of vibrating the sample 102 at afew kHz to several tens of MHz frequencies. The sample holder 404includes a base 106, a metal layer 402 and a first excitation source,such as a bimorph/piezoelectric crystal (PZT) oscillator 108. Theposition of the probe 112-114 with respect to the sample base 106 can bechanged in the x-y direction (depending on the AFM system used, eitherthe cantilever or the sample can be moved in x-y direction). The PZToscillator 108 is glued to the base 106 at a location that enablesexcitation of the sample 102 from the bottom of the sample 102, in orderto access subsurface information. The PZT oscillator 108 can generationvibrational energies having frequencies in the range of a few kHz totens of MHz, wherein the limit on its frequency is imposed by thebandwidth of the other pieces of equipment of the system 400.

As shown in FIG. 9, the sample 102 is near, but not in contact with atip 112 of a microcantilever 114 of an atomic force microscope (AFM).The AFM can be a commercial product such as the Multimode system made byVeeco with a Nanoscope III controller (but it is not restricted to thismodel). The microcantilever 114 is made of a conductive material and isbiased along with metal layer 402 with a potential source, such as apower supply 405 to create a system where the electrostatic forces arepredominant. As shown in FIG. 9, a second excitation source, such as aPZT oscillator 116, is coupled to the microcantilever 114. A lightsource, such as laser diode 118, generates a beam 120 of light that isdirected toward the microcantilever 114 and is reflected toward adetector, such as a four-quadrant photodetector 122. The reflected beamcontains information regarding the deflection undergone by themicrocantilever 114. A mirror or other optical elements may direct thereflected light toward the photodetector 122. Besides the abovedescribed optical deflection system, it would be possible to use apiezoresistive or piezoelectric method, in which case themicrocantilever 114 would be of different composition.

In operation, the PZT oscillator 108 is controlled by n functiongenerators FG_(is) (i=1, 2, 3, . . . n) represented collectively by box126 so that the PZT oscillator 108 generates multiple vibrational wavesat multiple frequencies f_(is) and amplitude a_(s). The waves havefrequencies f_(is) that range from a few kHz to several tens of MHz. Thewaves travel through the sample 102 and are sensed up by themicrocantilever 114. In addition, the mechanical oscillations caused byoscillators 108 and 116 induce a modulated electrostatic force that willlead to a nonlinear interaction between the sample 102 andmicrocantilever 114. The nonlinear interaction is composed of van derWaal-type and Coulomb-type contributions, wherein the Coulomb-typecontribution will be dominate depending on the strength of the electricfields. The amplitude and phase of the wave at a given frequency aredetected via the motion of the tip 112. Note that function generatorsFG_(is) can be replaced by a single programmable function generator thatcan handle multifrequency waveforms.

As shown in FIG. 9, a second PZT oscillator 116 is glued to themicrocantilever 114. The PZT oscillator 116 is connected to n functiongenerators FG_(ip) (i=1, 2, 3, . . . n) represented collectively by box136 so that the PZT oscillator 116 generates multiple wave formsacoustic waves at multiple frequencies f_(ip) and amplitude a_(p). Thefrequencies f_(ip) are generated independently of the frequenciesf_(is). The frequencies f_(ip) range from a few kHz to several tens ofMHz. In order to read out the deflection of the microcantilever 114, theoptical detection system is generally used as described previously.Motion of the tip 112 can also be detected by the piezoresistive methodor the piezoelectric method described previously. Note that functiongenerators FG_(ip) can be replaced by a single programmable functiongenerator that can handle multifrequency waveforms.

A coupling C, such as that described previously, is achieved by theanalysis system 400. The coupling C is determined from the signal S(t)generated by detector 122. The signal is sent to the controller 138monitors the feedback loop that controls the Z-position of thecantilever and converts the signal S(t) into display of a 2D image. Thesignal is sent to a spectrum analyzer 145 to identify the spectrum offrequencies representative of the multi-order coupling in the Fourierspace. The signal is sent to a lock-in amplifier 140 as well to monitorthe amplitude and phase of a given component of the S(ω) (i.e. one ofthe peaks observed on the spectrum analyzer). The lock-in amplifier 140sends amplitude and phase information/signals to a processor 141(generally the processor is included in the controller 138) thatdetermines an image of the sample 102 corresponding the response of thesystem at the given frequency used as reference in the lock-in. Thespectrum determined by spectrum analyzer 145 and the image of the sample102 determined by processor 141 can be displayed on display 143.

Other analyses performed by the analysis system 400 are possible. Forexample, the system 400 can be operated using the AFM and dataacquisition software such as Labview, and a Signal Access Module (SAMfrom Veeco), which allow external signals to be sent back to thecontroller 138 to be displayed at display 143. The information providedthrough the AFM software are: 1) the topography of the sample and 2) theresponse of the sample to the electric field oscillations for eachcomponent (frequency) generated by the nonlinear coupling and associatedto the electrostatic properties of the sample. The information providedthrough the data acquisition system software will include maps of thecontribution of a given frequency to the complex coupling between thetip 112 of the microcantilever 114 and the sample 102. This will includeamplitude and phase measurements with respect to the C-modes over the(driving) frequency ranges and (driving) amplitudes ranges. It can alsoinclude monitoring of the evolution of the amplitude and phase of thesignal at a given frequency as a function of the position of themicrocantilever 114 with respect to position (X, Y, Z) of the sample 102or with respect to time. The study of the deflection of themicrocantilever 114 as a function of Z is used to study the mechanicalproperties of the sample 102.

Another analysis system is shown in FIG. 10. As shown in FIG. 10,analysis system 500 is a variation of analysis system 100, wherein theorganic or inorganic sample 102 is thermally and mechanically excited bya first excitation source, such as light source 502, instead of by PZToscillator 108. In this embodiment, the light source 502 can be a laseror a spectrometer light source, wherein it can emit either a beam oflight with a fixed frequency or a beam of light composed of multiplewavelengths. The beam of light 504 emitted by the light source 502 ismodulated by a tunable modulator 506. The tunable modulator 506 can be amechanical chopper when kHz frequency light is emitted by light source502. The tunable modulator 506 can be an acousto-optic modulator orpulsed laser when higher frequencies of light are emitted by lightsource 502. The chopper is used in order to perform lock-in measurements(necessary for low level noisy signals), and to limit the heating of thesample.

As shown in FIG. 10, the sample 102 is in contact with a tip 112 of amicrocantilever 114 of an atomic force microscope (AFM). The AFM can bea commercial product such as the Multimode system made by Veeco with aNanoscope III controller (but it is not restricted to this model). Asshown in FIG. 10, a second excitation source, such as a PZT oscillator116, is coupled to the microcantilever 114. A light source, such aslaser diode 118, generates a beam 120 of light that is directed towardthe microcantilever 114 and is reflected toward a detector, such as afour-quadrant photodetector 122. The reflected beam contains informationregarding the deflection undergone by the microcantilever 114. A mirroror other optical elements may direct the reflected light toward thephotodetector 122. Besides the above described optical deflectionsystem, it would be possible to use a piezoresistive or piezoelectricmethod, in which case the microcantilever 114 would be of differentcomposition.

In operation, the tunable modulator 506 is controlled by n functiongenerators FG_(is) (i=1, 2, 3, . . . n) represented collectively by box526 so that the light source 502 generates multiple waves at multiplefrequencies f_(is) and intensities l_(is). The waves have frequenciesf_(is) that range from a few kHz to several tens of MHz depending on thethermal and optical properties. The waves travel through the sample 102and generate oscillations via the heat generated that are sensed up bythe microcantilever 114. In addition, the mechanical oscillations causedby the light source 502 and oscillator 116 create a nonlinearinteraction between the sample 102 and microcantilever 114. Theamplitude and phase of a wave at a given frequency are detected via themotion of the tip 112. Note that function generators FG_(is) can bereplaced by a single programmable function generator that can handlemultifrequency waveforms.

As shown in FIG. 10, PZT oscillator 116 is glued to the microcantilever114. The PZT oscillator 116 is connected to n function generatorsFG_(ip) (i=1, 2, 3, . . . n) represented collectively by box 136 so thatthe PZT oscillator 116 generates multiple wave forms acoustic waves atmultiple frequencies f_(ip) and amplitude a_(p). The frequencies f_(ip)are generated independently of the frequencies f_(is). The frequenciesf_(ip) range from a few kHz to several tens of MHz. In order to read outthe deflection of the microcantilever 114, the optical detection systemis generally used as described previously. Motion of the tip 112 canalso be detected by the piezoresistive method or the piezoelectricmethod described previously. Note that function generators FG_(ip) canbe replaced by a single programmable function generator that can handlemultifrequency waveforms.

A coupling C, such as that described previously, is achieved by theanalysis system 500. The coupling C is determined from the signal S(t)generated by detector 122. The controller 138 monitors the feedback loopthat controls the Z-position of the cantilever and converts the signalS(t) into display of a 2D image. The signal is sent to a spectrumanalyzer 145 to identify the spectrum of frequencies representative ofthe multi-order coupling in the Fourier space. The signal is sent to alock-in amplifier 140 as well to monitor the amplitude and phase a givencomponent of the S(ω) (i.e. one of the peaks observed on the spectrumanalyzer), relative to the nonlinear multi-order coupling resulting fromthe excitation of the microcantilever 114 and the sample 102 brought incontact with one another. The lock-in amplifier 140 sends amplitude andphase information/signals to a processor 141 (generally the processor isincluded in the controller 138) that determines an image of the sample102 corresponding the response of the system at the given frequency usedas reference in the lock-in. The spectrum determined by spectrumanalyzer 145 and the image of the sample 102 determined by processor 141can be displayed on display 143.

Other analyses performed by the analysis system 500 are possible. Forexample, the system 500 can be operated using the AFM and dataacquisition software such as Labview, and a Signal Access Module (SAMfrom Veeco), which allow external signals to be sent back to thecontroller 138 to be displayed at display 143. The information providedthrough the AFM software are: 1) the topography of the sample, and 2)the response of the sample to the mechanical oscillations for eachcomponent (frequency) enhanced by the nonlinear coupling to the lightexcitation. The information provided through the data acquisition systemsoftware will include maps of the contribution of a given frequency tothe complex coupling between the tip 112 of the microcantilever 114 andthe sample 102. This will include amplitude and phase measurements withrespect to the C-modes over the (driving) frequency ranges and (driving)amplitudes ranges. It can also include monitoring of the evolution ofthe amplitude and phase of the signal at a given frequency as a functionof the position of the microcantilever 114 with respect to position (X,Y, Z) of the sample 102 or with respect to time. The study of thedeflection of the microcantilever 114 as a function of Z is used tostudy the mechanical properties of the sample 102. The analysis system500 will provide chemical information on the composition of the sampleas a result of the sensitivity of the C-modes to temperature changes andphysical properties changes in the material exposed to the light. Thesystem 500 can be used to map the response of the sample illuminatedwith a fixed wavelength or a obtained a full spectrum of the material atthe position where the tip is located.

Another analysis system is shown in FIG. 11. As shown in FIG. 11,analysis system 600 is a variation of analysis system 500, wherein theorganic or inorganic sample 102 is thermally excited by a firstexcitation source, such as light source 502, and mechanically excited bya second excitation source, such as PZT oscillator 108. In thisembodiment, the light source 502 can be a laser or a spectrometer lightsource, wherein it can emit either a beam of light with a fixedfrequency or a beam of light composed of multiple wavelengths. The beamof light 504 emitted by the light source 502 is modulated by a tunablemodulator 506 and is directed to the top surface of the sample 102. Thetunable modulator 506 can be a mechanical chopper when kHz frequencylight is emitted by light source 502. The tunable modulator 506 can bean acousto-optic modulator or pulsed laser when higher frequencies oflight are emitted by light source 502. The chopper is used in order toperform lock-in measurements (necessary for low level noisy signals),and to limit the heating of the sample.

As shown in FIG. 11, the sample 102 is in contact with a tip 112 of amicrocantilever 114 of an atomic force microscope (AFM). The AFM can bea commercial product such as the Multimode system made by Veeco with aNanoscope III controller (but it is not restricted to this model). Asshown in FIG. 11, PZT oscillator 108 is coupled to the bottom surface ofthe sample 102. The oscillations generated by the light source 502 andthe PZT oscillator 108 are detected by the tip 112 of themicrocantilever 114. A second light source, such as laser diode 118,generates a beam 120 of light that is directed toward themicrocantilever 114 and is reflected toward a detector, such as afour-quadrant photodetector 122. The reflected beam contains informationregarding the deflection undergone by the microcantilever 114. A mirroror other optical elements may direct the reflected light toward thephotodetector 122. Besides the above described optical deflectionsystem, it would be possible to use a piezoresistive or piezoelectricmethod, in which case the microcantilever 114 would be of differentcomposition.

In operation, the tunable modulator 506 is controlled by n functiongenerators FG_(ip) (i=1, 2, 3, . . . n) represented collectively by box636 so that the light source 502 generates multiple waves at multiplefrequencies f_(ip), and intensities l_(ip). The function generators 636are similar to function generators 526 of FIG. 10. The waves havefrequencies f_(ip) that range from a few kHz to several tens of MHzdepending on the thermal and optical properties. The waves interact withthe sample 102 so as to generate oscillations via the heat generatedthat are sensed up by the microcantilever 114. Note that functiongenerators FG_(ip) can be replaced by a single programmable functiongenerator that can handle multifrequency waveforms.

As shown in FIG. 11, PZT oscillator 108 is connected to n functiongenerators FG_(is) (i=1, 2, 3, . . . n) represented collectively by box126 so that the PZT oscillator 108 generates multiple vibrationalenergies in the way of waves having multiple frequencies f_(ip) andamplitude a_(p). The frequencies f_(is) are generated independently ofthe frequencies f_(ip). The frequencies f_(is) range from a few kHz toseveral tens of MHz. In order to read out the deflection of themicrocantilever 114, the optical detection system is generally used asdescribed previously. Motion of the tip 112 can also be detected by thepiezoresistive method or the piezoelectric method described previously.Note that function generators FG_(is) can be replaced by a singleprogrammable function generator that can handle multifrequencywaveforms.

A coupling C, such as that described previously, is achieved by theanalysis system 600. The coupling C is determined from the signal S(t)generated by detector 122. The controller 138 monitors the feedback loopthat controls the Z-position of the cantilever and converts the signalS(t) into display of a 2D image. The signal is sent to a spectrumanalyzer 145 to identify the spectrum of frequencies representative ofthe multi-order coupling in the Fourier space. The signal is sent to alock-in amplifier 140 as well to monitor the amplitude and phase a givencomponent of the S(ω) (i.e. one of the peaks observed on the spectrumanalyzer), relative to the nonlinear multi-order coupling resulting fromthe excitation of the microcantilever 114 and the sample 102 brought incontact with one another. The lock-in amplifier 140 sends amplitude andphase information/signals to a processor 141 (generally the processor isincluded in the controller 138) that determines an image of the sample102 corresponding the response of the system at the given frequency usedas reference in the lock-in. The spectrum determined by spectrumanalyzer 145 and the image of the sample 102 determined by processor 141can be displayed on display 143.

Other analyses performed by the analysis system 600 are possible. Forexample, the system 600 can be operated using the AFM and dataacquisition software such as Labview, and a Signal Access Module (SAMfrom Veeco), which allow external signals to be sent back to thecontroller 138 to be displayed at display 143. The information providedthrough the AFM software are: 1) the topography of the sample, and 2)the response of the sample to the mechanical oscillations for eachcomponent (frequency) enhanced by the nonlinear coupling to the lightexcitation. The information provided through the data acquisition systemsoftware will include maps of the contribution of a given frequency tothe complex coupling between the tip 112 of the microcantilever 114 andthe sample 102. This will include amplitude and phase measurements withrespect to the C-modes over the (driving) frequency ranges and (driving)amplitudes ranges. It can also include monitoring of the evolution ofthe amplitude and phase of the signal at a given frequency as a functionof the position of the microcantilever 114 with respect to position (X,Y, Z) of the sample 102 or with respect to time. The study of thedeflection of the microcantilever 114 as a function of Z is used tostudy the mechanical properties of the sample 102. The analysis system600 will provide chemical information on the composition of the sampleas a result of the sensitivity of the C-modes to temperature changes andphysical properties changes in the material exposed to the light. Thesystem 600 can be used to map the response of the sample illuminatedwith a fixed wavelength or a obtained a full spectrum of the material atthe position where the tip is located.

Another analysis system is shown in FIG. 12. As shown in FIG. 12,analysis system 700 is a variation of analysis systems 500 and 600,wherein the organic or inorganic sample 102 is thermally excited both atits top and bottom surfaces by an excitation source, such as lightsource 502. In this embodiment, the light source 502 can be a laser or aspectrometer light source, wherein it can emit either a beam of lightwith a fixed frequency or a beam of light composed of multiplewavelengths. The beam of light 504 emitted by the light source 502 ismodulated by a tunable modulator 506. The modulated light is directed tothe bottom and top surfaces of the sample 102 by a beam splitter 702 andoptics, such as a plurality of mirrors 704. Accordingly, each split beamacts as a separate excitation source. The coherence (and phasedifference) between modulated light sent to the top and bottom surfacesof the sample 102 is used appropriately. The tunable modulator 506 canbe a mechanical chopper when kHz frequency light is emitted by lightsource 502. The tunable modulator 506 can be an acousto-optic modulatoror pulsed laser when higher frequencies of light are emitted by lightsource 502. The chopper is used in order to perform lock-in measurements(necessary for low level noisy signals), and to limit the heating of thesample.

As shown in FIG. 12, the sample 102 is in contact with a tip 112 of amicrocantilever 114 of an atomic force microscope (AFM). The AFM can bea commercial product such as the Multimode system made by Veeco with aNanoscope III controller (but it is not restricted to this model). Theoscillations generated by the light striking the bottom and top surfacesof the sample 102 are detected by the tip 112 of the microcantilever114. A second light source, such as laser diode 118, generates a beam120 of light that is directed toward the microcantilever 114 and isreflected toward a detector, such as a four-quadrant photodetector 122.The reflected beam contains information regarding the deflectionundergone by the microcantilever 114. A mirror or other optical elementsmay direct the reflected light toward the photodetector 122. Besides theabove described optical deflection system, it would be possible to use apiezoresistive or piezoelectric method, in which case themicrocantilever 114 would be of different composition.

In operation, the tunable modulator 506 is controlled by n functiongenerators FG_(i) (i=1, 2, 3, . . . n) represented collectively by box636 so that the light source 502 generates multiple waves at multiplefrequencies f_(is) and intensities l_(ip). The light beams createexcitation energies having frequencies f_(i) that range from a few kHzto several tens of MHz depending on the thermal and optical properties.The waves interact with the sample 102 so as to generate oscillationsvia the heat generated that are sensed up by the microcantilever 114.Note that function generators FG_(i) can be replaced by a singleprogrammable function generator that can handle multifrequencywaveforms.

A coupling C, such as that described previously, is achieved by theanalysis system 700. The coupling C is determined from the signal S(t)generated by detector 122. The controller 138 monitors the feedback loopthat controls the Z-position of the cantilever and converts the signalS(t) into display of a 2D image. The signal is sent to a spectrumanalyzer 145 to identify the spectrum of frequencies representative ofthe multi-order coupling in the Fourier space. The signal is sent to alock-in amplifier 140 as well to monitor the amplitude and phase a givencomponent of the S(ω) (i.e. one of the peaks observed on the spectrumanalyzer), relative to the nonlinear multi-order coupling resulting fromthe excitation of the microcantilever 114 and the sample 102 brought incontact with one another. The lock-in amplifier 140 sends amplitude andphase information/signals to a processor 141 (generally the processor isincluded in the controller 138) that determines an image of the sample102 corresponding the response of the system at the given frequency usedas reference in the lock-in. The spectrum determined by spectrumanalyzer 145 and the image of the sample 102 determined by processor 141can be displayed on display 143.

Other analyses performed by the analysis system 700 are possible. Forexample, the system 700 can be operated using the AFM and dataacquisition software such as Labview, and a Signal Access Module (SAMfrom Veeco), which allow external signals to be sent back to thecontroller 138 to be displayed at display 143. The information providedthrough the AFM software are: 1) the topography of the sample, and 2)the response of the sample to the mechanical oscillations for eachcomponent (frequency) enhanced by the nonlinear coupling to the lightexcitation. The information provided through the data acquisition systemsoftware will include maps of the contribution of a given frequency tothe complex coupling between the tip 112 of the microcantilever 114 andthe sample 102. This will include amplitude and phase measurements withrespect to the C-modes over the (driving) frequency ranges and (driving)amplitudes ranges. It can also include monitoring of the evolution ofthe amplitude and phase of the signal at a given frequency as a functionof the position of the microcantilever 114 with respect to position (X,Y, Z) of the sample 102 or with respect to time. The study of thedeflection of the microcantilever 114 as a function of Z is used tostudy the mechanical properties of the sample 102. The analysis system700 will provide chemical information on the composition of the sampleas a result of the sensitivity of the C-modes to temperature changes andphysical properties changes in the material exposed to the light. Thesystem 700 can be used to map the response of the sample illuminatedwith a fixed wavelength or a obtained a full spectrum of the material atthe position where the tip is located.

An analysis system 800 is shown in FIG. 13. In this embodiment, theinorganic or organic sample 102 is attached to a first excitationsource, such as a bimorph/piezoelectric crystal (PZT) oscillator 808.The PZT oscillator 108 enables vibrational excitation of the sample 102from the bottom of the sample 102, in order to access subsurfaceinformation. The PZT oscillator 108 can be in the range of a few kHz totens of MHz, wherein the limit on its frequency is imposed by thebandwidth of the other pieces of equipment of the system 800. Theoscillator 808 can have an opening 802 that receives light 804therethrough so that the sample 102 is heated. Although the coupling isgenerated by the mechanical excitation of the probe and the sample incontact, the illumination of the sample by a light source 804 willaffect the amplitude and the phase of the coupling. This analysis systemcan be configured with or without the chopper described in FIG. 11.

As shown in FIG. 13, the sample 102 is in contact with a tip 112 of amicrocantilever 114 of an atomic force microscope (AFM). The AFM can bea commercial product such as the Multimode system made by Veeco with aNanoscope III controller (but it is not restricted to this model). Asshown in FIG. 13, a second excitation source, such as a PZT oscillator116, is coupled to the microcantilever 114. A light source, such aslaser diode 118, generates a beam 120 of light that is directed towardthe microcantilever 114 and is reflected toward a detector, such as afour-quadrant photodetector 122. The reflected beam contains informationregarding the deflection undergone by the microcantilever 114. A mirroror other optical elements may direct the reflected light toward thephotodetector 122. Besides the above described optical deflectionsystem, it would be possible to use a piezoresistive or piezoelectricmethod, in which case the microcantilever 114 would be of differentcomposition.

In operation, the PZT oscillator 108 is controlled by n functiongenerators FG_(is) (i=1, 2, 3, . . . n) represented collectively by box126 so that the PZT oscillator 808 generates multiple vibrationalenergies in the form of waves at multiple frequencies f_(is) andamplitude a_(s). The waves have frequencies f_(is) that range from a fewkHz to several tens of MHz. The waves travel through the sample 102 andare sensed by the microcantilever 114. The amplitude and phase of a waveat a given frequency are detected via the motion of the tip 112. Notethat function generators FG_(is) can be replaced by a singleprogrammable function generator that can handle multifrequencywaveforms.

As shown in FIG. 13, the PZT oscillator 116 is glued to themicrocantilever 114. The PZT oscillator 116 is connected to n functiongenerators FG_(ip) (i=1, 2, 3, . . . n) represented collectively by box136 so that the PZT oscillator 116 generates multiple vibrationalenergies in the form of waves at multiple frequencies f_(ip) andamplitude a_(p). The frequencies f_(ip) are generated independently ofthe frequencies f_(is). The frequencies f_(ip) range from a few kHz toseveral tens of MHz. In order to read out the deflection of themicrocantilever 114, the optical detection system is generally used asdescribed previously. Motion of the tip 112 can also be detected by thepiezoresistive method or the piezoelectric method described previously.Note that function generators FG_(ip) can be replaced by a singleprogrammable function generator that can handle multifrequencywaveforms.

A coupling C, such as that described previously, is achieved by theanalysis system 800. The coupling C is determined from the signal S(t)generated by detector 122. The controller 138 monitors the feedback loopthat controls the Z-position of the cantilever and converts the signalS(t) into display of a 2D image. The signal is sent to a spectrumanalyzer 145 to identify the spectrum of frequencies representative ofthe multi-order coupling in the Fourier space. The signal is sent to alock-in amplifier 140 as well to monitor the amplitude and phase a givencomponent of the S(ω) (i.e. one of the peaks observed on the spectrumanalyzer), relative to the nonlinear multi-order coupling resulting fromthe excitation of the microcantilever 114 and the sample 102 brought incontact with one another. The lock-in amplifier 140 sends amplitude andphase information/signals to a processor 141 (generally the processor isincluded in the controller 138) that determines an image of the sample102 corresponding the response of the system at the given frequency usedas reference in the lock-in. The spectrum determined by spectrumanalyzer 145 and the image of the sample 102 determined by processor 141can be displayed on display 143.

Other analyses performed by the analysis system 800 are possible. Forexample, the system 800 can be operated using the AFM and dataacquisition software such as Labview, and a Signal Access Module (SAMfrom Veeco), which allow external signals to be sent back to thecontroller 138 to be displayed at display 143. The information providedthrough the AFM software is: 1) the topography of the sample, 2) theresponse of the sample to the mechanical oscillations for each component(frequency) generated by the nonlinear coupling. The informationprovided through the data acquisition system software will include mapsof the contribution of a given frequency to the complex coupling betweenthe tip 112 of the microcantilever 114 and the sample 102. This willinclude amplitude and phase measurements with respect to the C-modesover the (driving) frequency ranges and (driving) amplitudes ranges. Itcan also include monitoring of the evolution of the amplitude and phaseof the signal at a given frequency as a function of the position of themicrocantilever 114 with respect to position (X, Y, Z) of the sample 102or with respect to time. The study of the deflection of themicrocantilever 114 as a function of Z is commonly called a “force curvemeasurement” and is used to study the mechanical properties of thesample 102.

With the above described MSAFM systems of FIGS. 1-13, variousinformation regarding the samples can be ascertained. For example, when“vibrational excitation” of the sample occurs, information regarding themechanical/physical properties can be obtained. When “electromagneticexcitation” of the sample occurs, electric/physical properties of thesample can be obtained and chemical information is obtained when lightis shone on the sample. In addition, various imaging information can begenerated, such as 1) subsurface scattering and imaging, 2) imaging ofnanofabricated samples, 3) imaging of biomass samples, as will bedescribed below 4) chemical information.

Subsurface Scattering and Imaging Using MSAFM

MSAFM relies on the C-modes to acquire subsurface information. Usingelastic excitation and therefore initially an “acoustic probe” to sensethe interior of the sample 102, the variation in the C-modes will thenregister the embedded inhomogeneities. In a hypothetical gedankenmeasurement scenario, in principle, using a sample's C-modes, one couldmeasure the presence of any nanoparticles within the material domain ofthe cantilever probe via the detection of an induced perturbation.However, in this gedanken experiment, one would need to be able todetect the local oscillation of the sample surface, near the contactpoint, with a comparable sensitivity to that of the cantilever. In anattempt to computationally visualize the subsurface elastic perturbationinduced by embedded nanoparticles that would give rise to a detectablesurface manifestation, altering the contact point dynamics (and thusaltering the C-modes attributes), the surface stress, surface velocity,deformation, and strain energy density of a cell-shaped silicon mediumthat has various shaped embedded nanomaterial inhomogeneities can besolved. The results are shown in FIGS. 14 a-c and clearly indicate thatthe embedded structures (triangle, square, and circles of differentmaterials) can engender, at the top surface of the embedding structure,a variation in the surface traction and the velocity. The right mostparticle has a Young modulus that is higher than the silicon matrix,while all the others have lower moduli. Note that FIG. 14 a is acalculation of surface traction, FIG. 14 b is a calculation of surfacevelocity measured at a segment of the top boundary of the surface shownin FIG. 14 c. Also, the sample 102 of FIG. 14 c containing thenanoparticles of three different geometries is elastically excited fromthe bottom layer. FIG. 14 c is a black and white picture of a coloredpicture representing the strain energy density, and the particular colorof the boundary of the sample and the nanoparticles indicate the totaldisplacement of the material. A brighter surface color indicates ahigher strain energy density due to its vicinity to the oscillatingboundary (substrate interface). A red boundary color for the embeddednanoparticles indicates a higher total displacement of the nanoparticleswhile a yellow color indicates a smaller displacement.

Imaging of Nanofabricated Samples Using MSAFM

In the case of imaging a nanofabricated sample, an example of ananofabricated sample contains subsurface material inhomogeneities inform of a matrix of nickel nanodots confined within a germanium coatingon quartz substrate. E-beam lithography can be used to create anembedded material feature that can be used to discern the synthesizedmodes by providing various surface and subsurface features of the buriedstructure. In particular, an embedding strategy (involving reactive ionetching (RIE)) that is intended to minimize the surface deformation dueto the embedded inhomogeneity can be used. The final metallization stageleaves the sample surface as a uniform featureless structure. As shownin FIGS. 15 a-d, the embedding strategy can include embedding theinhomogenities in a 3×2 matrix pattern, wherein the three inhomogenitiesin the top row are identified by numerals 1-3 read from left to right.The bottom row of inhomogenities is similarly identified as 4-6. Asshown in FIGS. 15 e-h, the embedding strategy can include imbedding theinhomogenities in a 3×3 matrix pattern, wherein the three inhomogenitiesin the top row are identified by numerals 1-3 read from left to right.The middle row and bottom row of inhomogenities are similarly identifiedas 4-6 and 7-9, respectively. The corresponding images acquired from themodes l−1_(s)1_(p)> (a), |2_(s)−1_(p)> (b), |1_(s) 0_(p)> (c), and|0_(s) 1_(p)> (d) by invoking a first set of frequencies; and |−1_(s)1_(p)> (e), |2_(s)−1_(p)> (f), |1_(s) 0_(p)> (g), |0_(s) 1_(p)> (h),|−1_(s) 2_(p)> (i), and |1_(s) 1p> (j) using a second set offrequencies, are shown in FIGS. 15 a-h. As can be observed by directcomparison between the topography image and those acquired from thesynthesized modes, the nanostructures (in particular FIGS. 15 d and f)are not apparent at the surface level. Thus, the level of concealmentappears satisfactory to probe the differences in the informationdelivered by the multitude of the synthesized modes. However,improvements in the fabrication can be made as the residues observed fordots 1, 2, 3, and 5 of the matrix are mainly due to non-optimizedfabrication parameters (for example if the hole/dot created in theconductive layer by RIE could not be filled at the appropriate levelover the matrix. While limited topographic features can be seen in FIG.15, the overall purpose of demonstrating the usefulness of MSAFM inbringing out the differences between the modes is achieved. All theimages presented in FIGS. 15 a-h result from measurements of theamplitudes of the synthesized modes of frequencies ω_(|isjp>). In thefirst set of data shown in FIGS. 15 a-d, although the amplitudes vary,the six nanostructures are visible in all four images. The images ofFIGS. 15 a and c exhibit common features by the virtue of the subsurfaceinformation. As shown in FIG. 15 d, a new perspective is delivered bymode |0_(s) 1_(p)> exposing the substrate and the nickel nanostructures.For the particular set of parameters chosen (excitation amplitude andfrequencies) and the used probe (k=0.06N/m), although the amplitudeassociated with |2_(s)−1_(p)> is not superior to those of the lowerorder couplings, all 6 nanostructures can also be resolved with a strongcontrast between the core of the dots and the rest of the sample.

Note that when a given synthesized mode corresponds to one of the manyresonances of the system, the corresponding signal will be of higheramplitude (see also FIG. 15). This is in particular important for softercantilevers. The peripheral features in the region around the dot, inparticular around positions 1 and 3, are associated with thenanofabrication process (electron diffusion, etching variation, etc). Inthe second set of data of FIGS. 15 e-h) acquired with another set ofexcitation amplitudes and frequencies, 9 nanostructures can bedistinguished, 6 of which (1-6) are similar to the ones presented in thefirst row of FIGS. 15 a-d. Note that, similar to FIG. 15 g and FIG. 15h, the contrast is inverted between the image of FIG. 15 e.

Imaging of Biomass Samples Using MSAFM

The chemically and morphologically complex Populus wood and plant cellsare currently of prime interest for biomass conversion. However, due tothis complexity, nondestructive characterization of such samples ischallenging and thus provides a superb opportunity for atomic forcemicroscopy. Indeed, an accurate model of the organization (chemical,structural, etc) of biomass at the cellular level is still missing,slowing progress towards overcoming recalcitrance. FIGS. 6 a-j furtherillustrate the performance of the MSAFM on a cross section of freshPopulus wood. From these images, both the complex structure of thesample at a given location, and the variations in morphology for thesame cross section are evident. For example, the average size of thecell walls in the region, where the bottom images of FIGS. 6 a-j areacquired, appears to be larger than seen in the top images. Topographyimages corresponding to the MSAFM images of FIGS. 6 a-j are presented inFIGS. 16 a-d. In FIGS. a-d, the middle lamella (L), the interstitialregion between different cell walls (CW); the secondary CW (SCW), thethickest layer of the plant CWs, are presented in light of the differenthigher order couplings of MSAFM. Here, the probe was driven at anamplitude of 10 Vpp, and the sample at an amplitude of 9 Vpp. Thespectrum, providing each C-mode invoked, is presented in FIG. 6.

Clearly, each of the MSAFM images highlights unique features of theplant cell walls, not retrievable from others by postprocessing. The AFMimage (topography as well as a larger scan of the same region) arepresented in FIGS. 16 a-d for comparison. The observed differences inthe textures and contrast in the MSAFM images of FIGS. 6 a-j are relatedto the properties of the sample and can be used to characterize thedifferent layers of the plant cell wall. The observation of an increasein the size of the CW may be described as due to the evolution of thePopulus system: the primary and secondary CWs are formed at differentstages in the evolution of the populus. Growing and dividing cells willbe composed of primary CW, which is thin and flexible. The stronger andmore rigid secondary CW will appear after maturation of the cell.Secondary CWs are abundant in poplar tissues and are rich in cellulose.The lamella is now believed to be rich in lignin and acts as a gluebetween the different cells of the plant. Such properties are reflectedin the MSAFM images as the observed differences in contrast and features

MSAFM allows both the amplitude and the phase of S(t) to be used tostudy the differences in the roughness, elasticity, viscosity,compliance, etc. In FIGS. 6 g-j, a larger CW [see FIGS. 16 c-d] of thesample is presented by invoking the C-modes: ω_(|−1p 1p)>=323 kHz (g),ω_(|2p-1p>)=677 kHz (h), ω_(|−1p 2p>)=1.646 MHz (i), andω_(|0p 2p>)=2.646 MHz (j), originating from the spectrum in FIG. 6 f.Both FIGS. 6 a and 6 g display a higher sensitivity to the roughness ofthe sample with FIG. 6 g revealing details that are absent in all theimages of FIGS. 6 h-j. The corresponding image from AFM does not resolvethese details (see FIGS. 16 a-d for AFM topography and FIG. 17 that isan image of the same area when both the cantilever and the sample areexcited). An impressive set of details of the sample can be observed.Cellulose microfibrils are present in FIGS. 6 a and 6 g in the regioncloser to the vacuole, indicative of the cellulose content of the SCW.Regions with different orientations of the cellulose microfibrils can beidentified from a careful inspection of the images. The differentproperties of the lamella (L) appear in FIGS. 6 a-f, in particular inFIG. 6 b. The SCW also appears as an inhomogeneous medium. FIGS. 6 c andd highlight other details of the CWs: FIG. 6 d is richer in the contrastand exhibits certain grain structure, especially in L, whereas thecontrast in FIG. 6 c tends to show that the amplitude of the signal ismore sensitive to the changes in height (dark regions) than FIGS. 6 a, band d. Indeed FIG. 6 c is the only image that does not exhibit a changeof color in the CW on the left (close to the green line), which isobservable in the others, especially in FIG. 6 d. Such parallel study ofthe various C-mode images helps differentiate the SCW, L, and CCregions. Notably, the difference in contrast and texture in the CC[bottom of FIGS. 6 c and d] is interesting, given the high lignincontent of this particular region, also observed in their Ramansignature. The images obtained without a direct subsurface contribution(probe excitation only), FIGS. 6 h-j, tend to respond strongly (highsignal is black on the bottom images) to edgy or particular structuresfor large and rough areas and potentially limiting the contrast forother areas of the sample.

Comparing FIGS. 6 h-j to the image obtained for the same parameters butalso with sample excitation (see FIG. 17), it is then possible toidentify subsurface features. Note that FIG. 17 displays an imageobtained from |0_(s)2_(p)> mode, to be compared to FIGS. 6 h-j. Notethat this mode is a result of the mixing <−1_(s)1_(p)|C¹+|1_(s)1_(p)>.The excitation of the sample in the case of MSAFM with two initialexcitations gives access to additional subsurface details when comparedto the image of the same region obtained for the same excitations (FIG.6 i) by driving only the cantilever (with two frequencies). A similarcomparison is shown in FIGS. 18 a-b, wherein FIG. 18 b is an MSAFM imageof a poplar cell wall in the configuration of three excitation statesthat define the |1_(p) −1_(p) 1_(s)> state and FIG. 18 a is a standardAFM topography image (7 μm scan size) of the same region of the poplarcell wall. The system in FIG. 3 is used to generate the results of FIGS.15, 17 and 18 b. Clearly, MSAFM opens a new dimension in the study ofnanoscale features of biomass. The images complement each other byhighlighting different properties simultaneously.

The foregoing description is provided to illustrate the invention, andis not to be construed as a limitation. Numerous additions,substitutions and other changes can be made to the invention withoutdeparting from its scope as set forth in the appended claims. Forexample, each of the embodiments of FIGS. 1-12 can be conducted in aliquid medium, and in particular, conducted in a fluid cell. Anotherexample would be to replace the PZTs of FIGS. 1-12 by surface acousticwaves (SAW) or quartz crystal microbalance (QCM). In such cases, for thestudy of the dynamics of the MSAFM, the cantilever probe will engage ininteraction with the surface of either the SAW or the QCM device. Thisinteraction is then modulated by the oscillations of the probe and/orSAW and QCM surfaces, giving rise to unique MSAFM C-modes. Inapplications, a sample under study will be immobilized on the surface ofthe QCM or SAW while the cantilever probe will come in contact withsample surface and engage in contact-mode interaction. Then oscillationsof the cantilever and the SAW or QCM devices will modulate theprobe-sample distance to generate operational MSAFM C-modes.

1-16. (canceled)
 17. A sensor system comprising: a first cantilevercomprising a first end; a first excitation source that applies to saidfirst cantilever a first set of energies at a first set of frequencies;a second cantilever comprising a second end, wherein said second end isadjacent to said first end; a second excitation source, independent ofsaid first excitation source, that applies a second set of energies at asecond set of frequencies, wherein said first set of energies and saidsecond set of energies are simultaneously applied to said firstcantilever and said second cantilever, respectively, and form amulti-mode coupling; and a detector that detects an effect of saidmulti-mode coupling.
 18. The sensor system of claim 17, wherein saidfirst set of energies is a first set of vibrational energies and saidsecond set of energies is a second set of vibrational energies.
 19. Thesensor system of claim 18, further comprising; a spectrum analyzer thatreceives a first signal from said detector; and a display that receivesa second signal from said spectrum analyzer and generates a spectrum ofsaid sample based on said second signal.
 20. The sensor system of claim18, further comprising; a lock-in amplifier that receives a first signalfrom said detector; a processor that receives a second signal from saidlock-in amplifier; and a display that receives a third signal from saidprocessor and generates an image of said sample based on said thirdsignal.
 21. The sensor system of claim 19, further comprising: a seconddetector; a second spectrum analyzer that receives a third signal fromsaid second detector; and a second display that receives a fourth signalfrom said second spectrum analyzer and generates a second spectrum ofsaid sample based on said fourth signal.
 22. The sensor system of claim20, further comprising; a second detector; a second lock-in amplifierthat receives a fourth signal from said detector; a second processorthat receives a fifth signal from said second lock-in amplifier; and asecond display that receives a sixth signal from said second processorand generates a second image of said sample based on said sixth signal.23. A method of analyzing a sample comprising: applying a first set ofenergies at a first set of frequencies to a sample via a firstcantilever; applying a second set of energies at a second set offrequencies to said sample via a second cantilever, wherein said firstcantilever is adjacent to said second cantilever, wherein said first setof energies and said second set of energies are simultaneously appliedto said first cantilever and said second cantilever, respectively, andform a multi-mode coupling; and detecting an effect of said multi-modecoupling.
 24. The method of claim 23, further comprising: displaying aspectrum of said sample based on said detecting.
 25. The method of claim23, wherein said first set of energies is a first set of vibrationalenergies and said second set of energies is a second set of vibrationalenergies. 26-36. (canceled)